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Calculus Review
Suppose we have a function of one variable f(x) = 5.5x – x
2
.
This function looks like this:
In economics we often have functions that we want to minimize or maximize. By maximize I
mean we want to know which value of x maximizes (in this example) f(x).
From our chart it
looks like the answer is around 3.
We can use calculus to get the exact answer.
At the exact point f(x) reaches its maximum its slope is equal to 0, we will exploit this fact to
solve many maximization (and minimization) problems.
In calculus the derivative of a function gives us a new function for the slope of the original
function.
Our function is f(x) = 5.5xx
2
.
We will denote the derivative of f(x) as f
x
(x) which is the formula for the slope of f(x).
f
x
(x) = 5.5 – 2x (see below for derivative rules)
For any value of x, say x = 1, I can now tell you what f(1) is and what the slope of the function is
at f(1).
f(1) = 5.5(1)– 1
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 Fall '09
 CONSIDINE,TIMOTHY

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